On a hybrid electric vehicle on which an internal combustion engine and an electric motor are installed, an electric vehicle (EV) mode travel using only the electric motor as power for travel and a hybrid electric vehicle (HEV) mode (HEV) travel using both the internal combustion engine and the electric motor as the power for travel are selectively applied. For that purpose, the internal combustion engine and the electric motor are connected by a clutch.
When a driver of the hybrid electric vehicle turns off an ignition key of the vehicle during the engine operation in a vehicle stop state, the fuel supply to the internal combustion engine stops under a state in which the clutch is engaged. In such a case, the hybrid electric vehicle according to JP 08-121203 A, published in 1996 by the Japan Patent Office, proposes to first disengage the clutch, and then stop the fuel supply to the internal combustion engine.